Question
The solid below is made from centimeter cubes.
Find its surface area.
Find its surface area.
Answers
GPT 3.5
To find the surface area of a solid made from centimeter cubes, we need to calculate the total number of centimeter cubes used to create the solid and then find the number of cubes on the surface.
From the image provided, it appears that the solid is a rectangular prism made up of 5 layers of 4x4 centimeter cubes.
So, the total number of centimeter cubes used to create the solid = 5 layers * 4 cubes/layer * 4 cubes/layer = 80 cubes
Now, let's find the number of cubes on the surface. Since the solid is a rectangular prism, the cubes on the top and bottom faces contribute 4 * 4 = 16 cubes each, and the cubes on the four side faces contribute 4 * 5 = 20 cubes each.
So, the total number of cubes on the surface = 2 * (16 cubes for the top and bottom faces) + 4 * (20 cubes for the side faces) = 2 * 16 + 4 * 20 = 32 + 80 = 112 cubes
Each cube has 6 faces. However, each cube on the interior of the solid will have 5 faces covered by neighboring cubes. So, to find the surface area, we need to subtract the faces that are not on the surface.
The surface area = Total number of cubes on the surface * 6 - Number of internal faces
= 112 * 6 - (80 * 1)
= 672 - 80
= 592 cm^2
Therefore, the surface area of the solid made from centimeter cubes is 592 cm^2.
From the image provided, it appears that the solid is a rectangular prism made up of 5 layers of 4x4 centimeter cubes.
So, the total number of centimeter cubes used to create the solid = 5 layers * 4 cubes/layer * 4 cubes/layer = 80 cubes
Now, let's find the number of cubes on the surface. Since the solid is a rectangular prism, the cubes on the top and bottom faces contribute 4 * 4 = 16 cubes each, and the cubes on the four side faces contribute 4 * 5 = 20 cubes each.
So, the total number of cubes on the surface = 2 * (16 cubes for the top and bottom faces) + 4 * (20 cubes for the side faces) = 2 * 16 + 4 * 20 = 32 + 80 = 112 cubes
Each cube has 6 faces. However, each cube on the interior of the solid will have 5 faces covered by neighboring cubes. So, to find the surface area, we need to subtract the faces that are not on the surface.
The surface area = Total number of cubes on the surface * 6 - Number of internal faces
= 112 * 6 - (80 * 1)
= 672 - 80
= 592 cm^2
Therefore, the surface area of the solid made from centimeter cubes is 592 cm^2.